Page 99 - Calculus Demystified

CHAPTER 3 Applications of the Derivative
86

Fig. 3.8

3.2 Maximum/Minimum Problems

One of the great classical applications of the calculus is to determine the maxima
and minima of functions. Look at Fig. 3.9. It shows some (local) maxima and (local)
minima of the function f .

Fig. 3.9
Notice that a maximum has the characterizing property that it looks like a hump:
the function is increasing to the left of the hump and decreasing to the right of the
hump. The derivative at the hump is 0: the function neither increases nor decreases